As more people are using the internet and smart phones many members of our stake are slowly moving away from the printed directories and using the online directory on lds.org. One issue we found, however, is that certain groups can not be entered.

For example contact information and address on the nearest temple, contact information for institute director (a senior missionary), contact information for the physical facilities management group (using church office phone, not home phone), and contact information for the mission office. Even having the phone number to the various meeting houses and family history libraries would be useful.

Is it possible to have this information listed somehow in the online directory?

To update the suggestion, make a directory of these contacts and post it as a "news" item for the stake. It won't be in the online directory, but it will be available online in a place that you probably want members to visit anyway.

Have you searched the Wiki?
Try using a Google search by adding "site:tech.lds.org/wiki" to the search criteria.